Differentiated product demand analysis with a structured covariance probit: A Bayesian econometric approach

Date of Completion

January 2009


Economics, General|Economics, Commerce-Business




This dissertation introduces a new structured-covariance heterogeneous-consumer probit discrete-choice demand model. The structured-covariance probit demand model is appropriate for consumers that view a product as spatially or symmetrically differentiated. To accomplish this it applies a location model that allows products to to vary in their location from one another in product characteristic space. The model allows consumers in the market to differ in the way they view the product as being differentiated. My probit model of demand imposes structure on the choice covariance matrix using a distance metric for product similarity. Choice covariance is modeled as a function of the distance between choices in product characteristic space. ^ The Bayesian framework is employed to conduct a unified approach for estimation and model evaluation. The structured covariance probit model is difficult if not impossible to estimate using classical methods. I explain Bayesian hierarchical specification and Markov Chain Monte Carlo (MCMC) simulation techniques for conducting inference on the model. This dissertation includes a detailed explanation of the methodological and programming details for estimating the model in an efficient way. In addition, a flexible specification for the distribution of consumer heterogeneity in preference is modeled with a Dirichlet process prior over normally distributed consumer segment clusters. This research evaluates whether the specification of the consumer preference distribution effects results guiding strategic market analysis. ^ I evaluate the performance of the probit demand model relative to the heterogeneous consumer logit demand model widely used by analyst for demand analysis. To verify model performance I conduct a sampling experiment. Then I present an empirical application using consumer panel data for the New York designated marketing area (DMA) on lemon-lime soda (un-cola) purchases. Results and analysis testify that the independence of irrelevant alternatives property - better known as IIA - inherent in the logit reveals itself in the heterogeneous consumer market demand rendition of the model. Most importantly I document that competitive effects captured by cross elasticities are largely preordained by the empirical definition of the outside good/no purchase option. On the other hand estimates of probit cross elasticities are found to be far more robust to definition of the outside good/no purchase option, making them superior demand models for empirical analysis. Results also indicate that the probit is superior for predicting demand in other markets because it captures the spatial differentiation of products at the consumer level. ^